Suppose we wanted to measure the temperature of a small quantity of water heated by a limited heat source.

1. To heat the water to the desired temperature using an external heater, it is necessary to heat the vessel, which in turn transfers heat to the water. The quantity of heat that must be added is related to the mass of the heater, plus the mass of the water, plus the mass of the vessel. The water is not heated directly by the heat source but by the vessel. Therefore we must include the specific heat of the vessel, the specific heat of the water, the mass of each, and the thermal conductivity between the vessel and the water. We should also consider the fact that while we are heating the vessel, it is losing heat to the atmosphere via conduction and radiation.
   
   
2. If we turn off the heat source when the water reaches the desired temperature it will begin to cool. The rate at which the temperature falls is related to:
   
   
1. The difference in temperature between the ambient air and the vessel's outer surface.
   
   
2. The thermal conductivity of the air, which is dependent on its moisture content.
   
   
3. The velocity of the ambient air surrounding the vessel: As the water cools,
   it heats the surrounding air. If the air is in motion, the rate of cooling is much faster than it is if the air is stagnant.
   
   
4. The thermal conductivity of the vessel: How well does it conduct the heat from the water?
   
   
5. The movement of the water in the vessel (is it being stirred?)
   
   
6. Convection within the vessel: External temperature gradients will conduct heat through the vessel walls at rates proportional to the temperature difference between the water and the external air. Such thermal gradients will set up convection currents inside the vessel.
   
   
3. If a thermometer is added through a port in the vessel, the water must give up the heat necessary to heat the thermometer. This is a function of the mass of the thermometer, its specific heat, and the thermal conductivity between the surface of the sensor and the sensing element within.
   
   
4. Additional heat must be supplied to maintain the thermometer at the water temperature. This is dependent on the amount of additional surface area the sensor presents to the ambient air and its thermal conductivity.

These considerations are mentioned not to complicate the discussion, but to point out how difficult it may be to answer simple-sounding questions relating to accuracy or speed of response. When faced with a limited heat source, it's important to restrict the mass and thermal conductivity of the sensor to minimize its effect on the temperature of the system.

In many practical applications it is necessary to measure the temperature of a small quantity of fluid or gas. Not only is the amount of available heat very small, but the temperatures within the system may be subject to rapid change. The guidelines are therefore:

	Minimize the mass of the sensor.
	Maximize the thermal conductivity of the tip of the sensor where the sensing element is closest to the process.
	Minimize the thermal conductivity of the sensor structure where it is not needed to conduct the heat from the process to the sensing element.